The sum of the 5th and 9th terms of an A.P is 40 and the sum of the 8th and 14th term is 64. Find the sum of first 20 terms.
Answers
Answer:
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Answer:
610
Step-by-step explanation:
Let first term = a and common difference = d.
According to formula,
nth term = a + (n - 1) d
5th term = a + (5 - 1) d = a + 4d
9th term = a + (9 - 1) d = a + 8d
8th term = a + 7d
14th term = a + 13d
According to first condition,
5th term + 9th term = 40
a + 4d + a + 8d = 40
2a + 12d = 40
Take 2 common from LHS
2(a + 6d) = 40
=> a + 6d = 20 ..... (I)
In the same we get the equation for the second condition.
a + 10d = 32 ...... (II)
Now we have 2 equations, so we can solve them simultaneously to get the value of a and d.
Subtract I from II.
=> 4d = 12
Therefore, d = 3
Now substitute d = 3 in I
a + 6(3) = 20
Therefore, a = 2
Now use the formula,
Sum of n terms of an AP = (2a + (n - 1) d) n / 2
= (2(2) + (20 - 1) * 3) * (20 / 2)
= (4 + 19 * 3) * 10
= (4 + 57) * 10
= 61 * 10
= 610
Ans: The Sum of the first 20 terms of this A.P. is 610.
Hope this helps